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ВИДЕОТЕКА |
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[Asymptotics beats Monte Carlo: The case of correlated local vol baskets] Christian Bayer Weierstrass Institute for Applied Analysis and Stochastics, Berlin |
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Аннотация: We consider a basket of stocks with both positive and negative weights, in the case where each asset has a smile, e.g., evolves according to its own local volatility and the driving Brownian motions are correlated. In the case of positive weights, the model has been considered in a previous work by Avellaneda, Boyer-Olson, Busca and Friz [Risk, 2004]. We derive highly accurate analytic formulas for the prices and the implied volatilities of such baskets. These formulas are based on a basket Carr-Jarrow formula, a heat kernel expansion for the (multi-dimensional) density of of the asset at expiry and the Laplace approximation. The formulas are almost explicit, up to a minimization problem, which can be handled with simple Newton iteration, coupled with good initial guesses as derived in the paper. Moreover, we also provide asymptotic formulas for the greeks. Numerical experiments in the context of the CEV model indicate that the relative errors of these formulas are of order Язык доклада: английский |